Precalculus Examples

$f (x) = \frac{(x + 3)}{(x^{2} + 6 x + 8)}$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{x + 3}{x^{2} + 6 x + 8}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$x + 3 = 0$

Step 1.2.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{(0) + 3}{{(0)}^{2} + 6 (0) + 8}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{0 + 3}{{(0)}^{2} + 6 (0) + 8}$

Step 2.2.2

Remove parentheses.

$y = \frac{0 + 3}{0^{2} + 6 (0) + 8}$

Step 2.2.3

Remove parentheses.

$y = \frac{(0) + 3}{{(0)}^{2} + 6 (0) + 8}$

Step 2.2.4

Simplify $\frac{(0) + 3}{{(0)}^{2} + 6 (0) + 8}$ .

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Step 2.2.4.1

Add $0$ and $3$ .

$y = \frac{3}{0^{2} + 6 (0) + 8}$

Step 2.2.4.2

Simplify the denominator.

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Step 2.2.4.2.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{3}{0 + 6 (0) + 8}$

Step 2.2.4.2.2

Multiply $6$ by $0$ .

$y = \frac{3}{0 + 0 + 8}$

Step 2.2.4.2.3

Add $0$ and $0$ .

$y = \frac{3}{0 + 8}$

Step 2.2.4.2.4

Add $0$ and $8$ .

$y = \frac{3}{8}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{8})$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0)$

y-intercept(s): $(0, \frac{3}{8})$

Step 4